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provided by University of Southern Queensland ePrints MNRAS 483, 1574–1581 (2019) doi:10.1093/mnras/sty3180 Advance Access publication 2018 November 29

The rotationally modulated polarization of ξ Boo A

1,2‹ 3 3 1,2

Daniel V. Cotton, Dag Evensberget, Stephen C. Marsden, Jeremy Bailey , Downloaded from https://academic.oup.com/mnras/article-abstract/483/2/1574/5218518 by University of Southern Queensland user on 14 November 2019 Jinglin Zhao,1 Lucyna Kedziora-Chudczer ,1,2 Bradley D. Carter,3 Kimberly Bott ,4,5 Aline A. Vidotto ,6 Pascal Petit,7,8 Julien Morin9 and Sandra V. Jeffers10 1School of Physics, UNSW Sydney, NSW 2052, Australia 2Australian Centre for Astrobiology, UNSW Sydney, NSW 2052, Australia 3University of Southern Queensland, Centre for Astrophysics, Springfield, Qld. 4300/Toowoomba, Qld. 4350, Australia 4University of Washington Astronomy Department, Box 351580, UW Seattle, WA 98195, USA 5NExSS Virtual Planetary Laboratory, Box 351580, UW Seattle, WA 98195, USA 6School of Physics, Trinity College Dublin, College Green, Dublin 2, Ireland 7Universite´ de Toulouse, UPS-OMP, IRAP, Toulouse F-31400, France 8CNRS, Institut de Recherche en Astrophysique et Planetologie, 14, avenue Edouard Belin, F-31400 Toulouse, France 9LUPM-UMR 5299, CNRS & Universite´ Montpellier, place Eugene` Bataillon, F-34095 Montpellier Cedex 05, France 10Institute for Astrophysics, University of Goettingen, Friedrich Hund Platz 1, D-37077 Goettingen, Germany

Accepted 2018 November 16. Received 2018 November 15; in original form 2018 September 25

ABSTRACT We have observed the active ξ Boo A (HD 131156A) with high precision broadband linear polarimetry contemporaneously with circular spectropolarimetry. We find both signals are modulated by the 6.43 d rotation period of ξ Boo A. The signals from the two techniques are 0.25 out of phase, consistent with the broadband linear polarization resulting from differential saturation of spectral lines in the global transverse magnetic field. The mean magnitude of the linear polarization signal is ∼4 ppm G–1 but its structure is complex and the amplitude of the variations suppressed relative to the longitudinal magnetic field. The result has important implications for current attempts to detect polarized light from hot Jupiters orbiting active in the combined light of the star and planet. In such work stellar activity will manifest as noise, both on the time-scale of , and on longer time-scales – where changes in activity level will manifest as a baseline shift between observing runs. Key words: polarization – stars: activity – stars: individual HD 131156A – stars: magnetic field.

in three, where the outside lines are polarized in one orientation 1 INTRODUCTION and the centre line – having double the intensity – is polarized The primary mode of characterizing the magnetic field in a star in the other (Stenflo 2013). When the magnetic field is weak, the is through circular polarimetry. In highly magnetic stars linear po- lines are not completely split, but instead the two components are larization may be used to complement measurements of circular to be found predominantly in the line wings and line core, re- polarization, and constrain magnetic field geometry (Wade et al. spectively. Spectropolarimetry – where the line profiles are fit to 2000 and references therein). However, modern stellar polarimeters determine polarization and hence magnetic field strength – can be are much more sensitive to circular polarization than to the inher- used to measure both types of polarization, but the line profiles of ently weaker signal from linear polarization. Only in the last decade circular polarization are much more easily detected (Wade et al. has linear polarization been definitively detected in (bright) weakly 2000). magnetic stars (Kochukhov & Wade 2010;Rosen,´ Kochukhov & In our recent paper we measured significant broadband linear Wade 2015). The difference arises as a result of the polarimetric polarization in a number of active late-type dwarf stars – mostly mechanism. In a magnetic field circular polarization is produced BY Dra variables and stars with emission line spectral types (Cot- by the longitudinal Zeeman effect splitting spectral lines into two ton et al. 2017b). In stars with very strong magnetic fields a net oppositely polarized (left and right handed) lines. Linear polariza- linear polarization will be measured in a line when the line core is tion is produced by the transverse Zeeman effect splitting lines saturated – called magnetic intensification (Babcock 1949). Sim- ilarly, ‘differential saturation’ describes the situation where many lines overlap and merge with each other (line blanketing) to pro-  E-mail: [email protected] duce a net broadband linear polarization (Bagnulo et al. 1995). The

C 2018 The Author(s) Published by Oxford University Press on behalf of the Royal Astronomical Society Polarization of ξ Boo A 1575 broadband linear polarization magnitude measured in the active Table 1. TP determination from low polarization standard observations. dwarfs was correlated with the maximum global longitudinal mag- Exposure times are 320 s for Sirius and 640 s otherwise. netic field (|B|max) from spectropolarimetric (circular polarimetry) measurements. Consequently it is presumed that the broadband lin- Star UTC q (ppm) u (ppm) ear polarization measured in these active dwarfs is produced through β Hyi 2017-06-22 19:21:20 − 25.9 ± 3.4 − 0.9 ± 3.3 differential saturation that is also induced by the global magnetic 2017-06-29 19:38:38 − 22.1 ± 5.0 1.1 ± 4.7 Downloaded from https://academic.oup.com/mnras/article-abstract/483/2/1574/5218518 by University of Southern Queensland user on 14 November 2019 field. If so, the field geometry will be important, a uniform dipolar 2017-06-30 19:50:35 − 15.8 ± 3.9 11.7 ± 3.8 field aligned with the stellar rotation axis might produce a constant 2017-08-11 16:26:58 − 21.5 ± 4.6 21.4 ± 4.4 polarization, more complicated structures will result in a time vary- 2017-08-11 17:48:42 − 19.0 ± 3.9 − 3.7 ± 4.0 ing signal. However, linear polarization may also be generated in 2017-08-17 19:24:21 − 31.5 ± 4.7 2.4 ± 5.2 active stars through other mechanisms with more complicated phase Sirius 2017-08-10 19:49:29 − 18.6 ± 3.6 6.2 ± 3.9 − ± − ± behaviour. Strong localized fields might be produced in starspots 2017-08-15 19:23:35 25.5 8.3 15.7 7.9 2017-08-16 19:27:41 − 19.5 ± 2.7 20.6 ± 3.6 (Huovelin & Saar 1991; Saar & Huovelin 1993). Or starspots might 2017-08-18 19:07:11 − 10.1 ± 12.2 12.8 ± 13.9 produce polarization by breaking symmetry, not in the spectral 2017-08-19 19:33:56 3.0 ± 2.3 − 9.0 ± 2.5 lines, but on the disc of the star instead (Yakobchuk & Berdyug- β Leo 2017-06-22 08:17:33 − 3.1 ± 2.4 − 6.0 ± 2.4 ina 2018). In red super/giant stars, stellar hotspots have also been 2017-06-26 08:17:37 − 8.0 ± 2.4 − 11.9 ± 2.2 found to produce linear polarization (Schwarz 1986;Auriere` et al. 2017-07-05 08:15:41 − 10.1 ± 3.4 − 7.8 ± 2.9 2016). β Vir 2017-06-23 08:14:32 − 2.7 ± 5.1 − 7.6 ± 4.9 Determining the polarimetric mechanism of the linear polariza- 2017-06-24 08:20:36 − 8.8 ± 4.6 − 5.7 ± 4.7 tion in active dwarfs is important, not just for the information com- Adopted TP − 15.0 ± 0.3 0.5 ± 0.3 plementary to spectropolarimetry (e.g. Wade et al. 1996;Rosen´ et al. 2015), but also because it is a potential source of noise in studying other polarimetric phenomena. In particular, a number of groups have been searching for the polarized light that is scattered 2 OBSERVATIONS from the atmosphere of a close hot Jupiter planet, in the combined light of the star and the planet (Lucas et al. 2009; Berdyugina et al. 2.1 Linear polarimetry 2011; Wiktorowicz et al. 2015;Bottetal.2018). If identified, such a signal can reveal details of the planet’s atmosphere: its albedo and Broadband linear polarization measurements were made with the cloud properties. However, stellar activity is likely to significantly HIgh Precision Polarimetric Instrument (HIPPI; Bailey et al. 2015) complicate such searches as the expected signal due to an orbit- on the 3.9-m Anglo-Australian Telescope, at Siding Spring Observa- ing, unresolved exoplanet is smaller than that seen in active dwarfs tory in Australia. The instrument was mounted at the F/8 Cassegrain (Seager, Whitney & Sasselov 2000; Bailey, Kedziora-Chudczer & focus, giving an aperture size of 6.7 arcsec – just small enough to Bott 2018), and many of the best candidate systems for detecting isolate ξ Boo A from ξ Boo B at the time of our observations a planetary signal (those with very short period planets orbiting (it is difficult to measure the seeing with HIPPI on the telescope bright stars) have late-type dwarf star hosts that are active or poten- accurately, but the seeing was decent – generally around 2 arcsec tially active. If activity effects are to be avoided, or removed, it is or better – for our observations). HIPPI has a night-to-night preci- important they be understood. sion of 4.3 ppm on bright stars, which it achieves using a (Boulder As the most polarized star identified in Cotton et al. (2017b) ξ Non-linear Systems) ferro-electric liquid crystal modulator operat- Boo A (HD 131156A) is the most obvious candidate to look for and ing at 500 Hz, and two additional slower stages of chopping (Bailey characterize any variability. It is a BY Dra (Samus’ et al. 2015). We configured HIPPI to use Hamamatsu H10720- et al. 2003) with a G7Ve spectral type (Levato & Abt 1978) lying 210 ultra bi-alkali photocathode photomultiplier tubes as detectors, 6.7 pc from the Sun (van Leeuwen 2007). It has a close companion and no photometric filter (Clear) – giving flux between 350 and which was 5.41 arcsec away (at the time of our observations), ξ Boo 730 nm. This is the usual configuration of the instrument for ob- B (HD 131156B), which is also an active star, of spectral type K5Ve servation of exoplanet systems, [e.g. the (inactive) WASP-18 sys- (Levato&Abt1978). ξ Boo A has a short, 6.43 d, rotational period tem; Bott et al. 2018]. For the G7 spectral type of ξ Boo A the (Toner & Gray 1988). In an early study Huovelin, Saar & Tuomi- effective wavelength is 486.1 nm and the modulation efficiency nen (1988) concluded that ξ Boo A varies in linear polarization 0.840. around its rotational cycle based on data greater than 2σ from the We observed ξ Boo A during two observing runs: 2017 June/July mean. and 2017 August. The telescope polarization (TP) is stable over Petit et al. (2005) found ξ Boo A has a magnetic field made such a time frame (Cotton et al. 2016a;Marshalletal.2016; Cotton up of two main components: a 40 G dipole inclined at 35◦ to the et al. 2017a,b), and was determined by taking the mean of all low rotation axis, and a large-scale 120 G toroidal field. Twenty polarization standard star observations. These are shown as normal- of data presented by Lockwood et al. (2007) show that its activity ized Stokes parameters in Table 1,whereq = Q/Iand u = U/I;the can vary on long time-scales in a seemingly irregular way. Similarly total linear polarization can be calculated as p = q2 + u2. Morgenthaler et al. (2012) present field maps corresponding to the The position angle (PA) was calibrated by reference to standard years 2007 to 2011 that show varying behaviour. On a shorter time- stars: HD 147084 (twice), HD 154445, and HD 160529 in June/July; scale, in 101 measurements, the BCool team (Marsden et al. 2014) and HD 147084, HD 154445, and HD 187929 in August. The ∼1◦ determined |B|max as 18.4 ± 0.3 G and |B|min as 0.5 ± 1.0 G. This error in the PA determination is dominated by the uncertainties is quite a strong field compared to other Solar type stars, but is still in the PAs of the standards (see Cotton et al. 2017a for standard a weak field compared to the fields found within star/sunspots or details). those in the hotter stars where linear polarimetry has traditionally Table 2 gives the ξ Boo A observations after PA calibration, been employed (Wade et al. 1996). subtraction of the TP, and efficiency correction.

MNRAS 483, 1574–1581 (2019) 1576 D. V. Cotton et al.

Table 2. HIPPI observations of ξ Boo A. Exposure time on 2017-08-14 the spectra around a set of known spectral lines from wavelength was 1000 s, but 800 s otherwise. pˆ is the intrinsic linear polarization (see space to velocity space and co-adds them to form one Stokes I and Section 3) debiased as pˆ = p2 − p2. one V line profile parametrized by Doppler velocity, each with a high S/N. UTC q (ppm) u (ppm) pˆ (ppm) As in the BCool survey (Marsden et al. 2014), ξ Boo A

2017-06-22 11:34:57 54.8 ± 6.5 − 20.9 ± 6.7 56.3 ± 7.3 stellar parameters from Valenti & Fischer (2005); Takeda et al. Downloaded from https://academic.oup.com/mnras/article-abstract/483/2/1574/5218518 by University of Southern Queensland user on 14 November 2019 −2 2017-06-24 11:14:51 23.3 ± 9.6 − 28.4 ± 11.5 61.9 ± 10.4 (2007): Teff = 5570 ± 31 K, log g = 4.57 ± 0.02 cm s ,and 2017-06-25 10:37:15 41.0 ± 7.0 15.5 ± 6.7 74.2 ± 8.0 log M/H =−0.07 ± 0.02, were used to determine the closest of ± ± ± 2017-06-26 09:34:48 44.2 7.3 10.3 7.1 45.2 9.4 the BCool atmospheric line masks, defined by Teff = 5500 K, 2017-06-29 11:45:04 42.0 ± 8.6 − 23.3 ± 9.1 66.7 ± 8.3 log (g) = 4.5 cm s−2,andlog(M/H) = 0, then used to generate 2017-06-30 11:07:24 35.9 ± 7.2 − 27.1 ± 7.4 37.8 ± 8.2 the Stokes I and V LSD profiles. The line mask originates from the ± ± ± 2017-07-01 11:06:51 29.0 6.6 1.4 6.7 42.4 8.0 Vienna Atomic Line Database (Kupka et al. 2000). ± − ± ± 2017-07-02 11:30:35 36.3 6.6 5.7 6.7 33.2 11.0 The mean longitudinal magnetic field is the line-of-sight mag- 2017-07-05 11:44:28 68.1 ± 7.3 − 34.9 ± 7.4 18.5 ± 8.2 netic field component integrated over the stellar disc. Following 2017-08-10 09:48:23 39.5 ± 7.0 5.7 ± 6.9 26.4 ± 7.4 2017-08-12 09:48:29 39.9 ± 7.6 11.2 ± 7.3 41.9 ± 7.6 Carroll & Strassmeier (2014), an estimate of this quantity can be 2017-08-14 09:47:14 34.1 ± 7.6 − 22.0 ± 7.6 32.1 ± 7.6 calculated directly from the LSD line profile: 2017-08-15 09:45:45 18.8 ± 7.7 − 11.7 ± 7.5 34.2 ± 7.4  h vV (v)dv 2017-08-16 09:49:53 34.7 ± 6.8 − 1.1 ± 6.9 43.2 ± 7.9 B =−  ,     − (1) 2017-08-19 09:50:30 55.7 ± 10.1 − 32.9 ± 9.6 37.6 ± 7.7 μB λ g Ic I(v)dv 2017-08-20 08:40:44 65.8 ± 7.7 − 21.0 ± 7.7 39.2 ± 8.1 where h is Planck’s constant and μB is the Bohr magneton. The parameters g and λ are the average Lande´ factor and wavelength Table 3. NARVAL observations of ξ Boo A and derived quantities. Lines taken over the spectral lines used in forming the LSD profile, and are the number of spectral lines with sufficient signal-to-noise ratio to be are calculated by LIBRE-ESPRIT for each observation (see Table 3). included when generating the LSD profile. The average Lande´ factor g We note that hc/μ = 0.0214 Tm, where c is the speed of light,   B and average central wavelength of lines used λ when generating the LSD permitting the recovery of the form of equation (1) (see Donati profile are used to calculate the mean longitudinal magnetic field B,see et al. 1997 where it is their equation 5, or Mathys 1989). equation (1). Due to the presence of noise, the calculation of B is affected by the range of velocities, v, over which the integrals in equation (1) UTC Lines gλ (nm) B (G)  are taken. The velocity range was chosen to maximize the periodic 2017-06-02 00:40:21 10769 1.215 560.9 +11.8 ± 0.7 signal when calculating a Lomb–Scargle periodogram. The lowest 2017-06-05 21:54:06 10773 1.215 547.5 +8.3 ± 3.7 false alarm probability of 3.0 per cent was found letting v range over 2017-06-06 21:24:20 10772 1.215 544.0 +11.4 ± 0.5 11 velocity bins centred on v = 1.8 km s−1. This gives a velocity + ± 2017-06-07 22:08:40 10779 1.215 546.7 15.7 0.5 line width for the Stokes I and V signals from −7.2 to 10.8 km s−1. + ± 2017-06-09 22:23:55 10773 1.214 550.7 3.2 1.1 The centre agrees well with the BCool astrometric 2017-06-10 22:24:20 10774 1.214 549.5 +5.8 ± 0.8 of 1.9 km s−1 (Marsden et al. 2014). 2017-06-11 23:24:59 10772 1.215 551.5 +9.3 ± 0.6 2017-06-12 22:22:54 10779 1.215 547.6 +9.9 ± 0.6 2017-06-13 23:15:23 10773 1.215 548.3 +16.2 ± 0.7 2017-06-14 22:21:13 10773 1.215 549.6 +13.5 ± 0.5 3ANALYSIS 2017-06-16 22:42:40 10778 1.215 546.1 +7.9 ± 0.5 2017-06-17 22:33:12 10771 1.215 545.9 +8.6 ± 0.5 The error weighted mean of the 16 HIPPI observations of ξ Boo A + ± is 41.4 ± 1.9 ppm in q and −9.1 ± 1.9 ppm in u.Thisisvery 2017-06-18 22:34:51 10771 1.215 547.5 9.5 0.5  2017-07-02 22:13:38 10775 1.215 555.7 +12.3 ± 0.7 similar to our previously reported observations in the SDSS g band 2017-07-05 22:15:22 10765 1.215 549.8 +3.2 ± 0.6 from 2016 February of 45.8 ± 5.2 and 3.0 ± 5.2 ppm, respec- tively (Cotton et al. 2017b). The effective wavelength of HIPPI’s  clear band (486.8 nm) is similar to that of the g band (472.4 nm); 2.2 Circular spectropolarimetry however, the clear band is much broader. Consequently, the differ- Spectropolarimetric observations were made with the NARVAL ence in these mean measurements is not sufficient to demonstrate echelle´ spectrometer operating at the Telescope´ Bernard Lyot (Ob- variability. servatoire du Pic du Midi, France). NARVAL (Donati et al. 2006) The interstellar polarization calculated for ξ Boo A is is a bench mounted spectrograph connected by optical fibre to a 1.7 ± 3.2 ppm in q and −0.9 ± 3.2 ppm in u (Cotton et al. Cassegrain mounted polarimetric module. The polarimetric module 2017b), based on its distance from the Sun of 6.7 pc and the comprises a series of Fresnel rhombs and a Wollaston prism. The PA of nearby intrinsically unpolarized stars. Thus it is very likely configuration permits the simultaneous recording of Stokes I and V the vast majority of polarization measured is intrinsic to the star. spectra. Each measurement comprises four exposures with different Subtracting the interstellar polarization and calculating the (debi- half-wave rhomb orientations to remove instrument effects (Semel, ased) linear polarization (pˆ) from q and u gives 40.5 ± 3.7 ppm Donati & Rees 1993; Donati et al. 1997). NARVAL covers the (we neglect the small effect from interstellar polarization colour wavelength range 370–1100 nm and has R ∼ 65000, corresponding – see Marshall et al. 2016 or Cotton et al. 2018 for a discus- to a pixel size of ∼1.8 km s−1 in velocity space. sion of the wavelength dependence of interstellar polarization for ξ Boo A was observed 15 times with NARVAL (Table 3). For nearby stars). The error weighted mean of B from the contempo- each observation, the resulting Stokes I and V spectra were reduced raneous NARVAL data is 10.7 ± 0.2 G, so if the intrinsic linear using least-squares deconvolution (LSD) with LIBRE-ESPRIT (Do- polarization is due to the magnetic field the mean contribution is nati et al. 1997 describes ESPRIT). The LSD technique transforms ∼3.8 ppm G–1.

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Table 4. Statistical analysis of linear polarization measurements. The error 3.2 Rotational modulation and the magnetic field weighted means (x¯wt ), means (x¯), mean errors (e¯), standard deviations (σ ), and error variances (s) are in ppm. Several determinations of the rotational period of ξ Boo A ex- ist. Using longitudinal magnetic field measurements Plachinda & ± Stokes x¯wt x¯ eσ¯ s Skewness Kurtosis Tarasova (2000) obtained 6.1455 0.0003 d. Activity indices based on Ca II H & K lines have been used by Noyes, Weiss & Vaughan

± Downloaded from https://academic.oup.com/mnras/article-abstract/483/2/1574/5218518 by University of Southern Queensland user on 14 November 2019 q 41.4 1.9 41.4 7.6 13.4 10.1 0.2272 2.6180 (1984): 6.2 ± 0.1, Donahue, Saar & Baliunas (1996): 6.31 d, and − ± − u 9.1 1.9 11.6 7.7 16.4 13.8 0.0475 1.6130 most recently Hempelmann et al. (2016): 6.299 ± 0.037. Toner & Gray (1988) made a careful analysis of line symmetry and line 3.1 Linear polarimetry statistics ratios to get 6.43 ± 0.01 d. The differences between these val- ues may be related to their probing of different stellar layers, and The average error in our linear polarization data – the internal the star’s differential rotation as described by Morgenthaler et al. standard deviation of individual measurements, which scales with (2012). We don’t have sufficient data to determine the period so photon-shot noise – is 7.6 ppm in q and 7.7 ppm in u. The standard precisely ourselves, so use our own period analysis to inform a deviation (or scatter, σ ) in repeat observations in both q and u choice. We first constructed a Lomb–Scargle periodogram with AS- is higher than this, which may indicate intrinsic variability. The TROPY’s ‘LombScargle’ package. Using the pˆ and B data, we find variability scale, sometimes called the error variance, is calculated   respectively ∼6.5 d and 6.3 d. We also applied Gaussian process as: maximum likelihood estimation (Fig. 1), finding 6.52 +0.05 dfor   −0.08 ± = 2 − 2 pˆ and 6.50 0.06 d for B. For this we used a combination of s σ δi , (2) i the exponential squared kernel and the exp-sine-squared kernel to describe the quasi-periodicity of the magnetic field, as well as a where δi values are known errors, here the average error (e¯), and rational-quadratic kernel that describes smooth signal changes at the night-to-night precision of HIPPI. Thus the error variance is various time-scales (Rasmussen & Williams 2006). We employed 10.1 ppm in q and 13.8 ppm in u. By comparison the standard the PYTHON library GEORGE (Ambikasaran et al. 2015) to implement deviation of the spectropolarimetric data is 4.0 G. If we scale this Gaussian processes and estimated the uncertainty of the period us- –1 value using the same ratio implied by the mean (3.8 ppm G )this ing Markov Chain Monte Carlo (MCMC) sampling with the EMCEE gives the equivalent of 15.2 ppm. PYTHON module (Foreman-Mackey et al. 2013). Consequently, as Table 4 presents the standard deviation, skewness, and kurtosis the best match for our data, we prefer the 6.43 d period of Toner & which characterize the variability in q and u. By comparison with Gray (1988) – as did Petit et al. (2005). the tables of Brooks, Clarke & McGale (1994) the kurtosis in u We phase-fold and plot the HIPPI data over the 6.43 d period in is non-Gaussian with 95 per cent, but not 99 per cent confidence – Fig. 2. We choose the first HIPPI observation as the (UTC: indicative of a centre-heavy distribution – but otherwise the data are 2017-06-22 11:34:57, JD: 2457926.9826). Data from parts of 10 consistent with being Gaussian. rotation cycles are shown, with points enumerated by cycle. The

Figure 1. The HIPPI pˆ (top) and NARVAL B (bottom) data (black) and the Gaussian process maximum likelihood prediction (grey) (and 1σ errors – light grey) used to determine periods. For comparison dashed lines show the chosen 6.43 d period.

MNRAS 483, 1574–1581 (2019) 1578 D. V. Cotton et al. Downloaded from https://academic.oup.com/mnras/article-abstract/483/2/1574/5218518 by University of Southern Queensland user on 14 November 2019

Figure 2. Phase-folded behaviour of ξ Boo A in q (top) and u (bottom), assuming a rotational period of 6.43 d. Numbers indicate the rotational cycle. It can be seen that there is an excellent agreement in both q and u between cycles, even after 10 cycles.

Figure 3. Top panel: phase-folded intrinsic linear polarization measured in ξ Boo A with HIPPI. Lower panel: the global longitudinal magnetic field (B) measured with NARVAL, offset in phase by 0.25. Shown on the plots are fitted sinusoids (black lines), fitted mean signals (dashed horizontal lines), fitted phases (dashed vertical lines), and their 1σ errors (grey panels). See also Table 5. later and earlier cycles match very well, confirming rotational is the global magnetic field of the star, then in the weak field case, modulation. √the transverse magnetic field strength (Bt) will be proportional to The shapes of the two fitted phase curves in Fig. 1 are notably p (Stenflo 2013). By definition Bt and B are orthogonal, so that similar, implying a common origin. If the polarimetric mechanism a point at the centre of the stellar disc contributing solely to B, will

MNRAS 483, 1574–1581 (2019) Polarization of ξ Boo A 1579

Table 5. Sinusoidal fitting of polarization measurements√ by equation (3). this situation when considering relatively strong fields in starspots.  The vertical offset, y0, and amplitude, A,are pˆ ( ) for HIPPI, and B Huovelin & Saar (1991) made calculations that show that for a (G) for NARVAL. The phases are given both in days (t0) and in phase units single small spot the linear polarization is greatest when the spot is (ϕ0). 45 deg from the disc centre (towards the limb); as larger spots are considered this approaches 90 degrees for spots up to 50 per cent Data set y0 At0 ϕ0 of the surface area – this being somewhat analogous to a global Downloaded from https://academic.oup.com/mnras/article-abstract/483/2/1574/5218518 by University of Southern Queensland user on 14 November 2019 HIPPI 6.61 ± 0.22 1.08 ± 0.28 4.50 ± 0.32 0.70 ± 0.05 field. However, no specific modelling of differential saturation has NARVAL 9.68 ± 0.67 4.44 ± 0.88 2.79 ± 0.23 0.43 ± 0.04 been done for weaker global fields, and it is possible other magneto- optical phenomena may play a role. For instance, if the polarization scales non-linearly with field strength (Stift 1997). Nevertheless, if contribute solely to Bt when at the limb. Consequently, B and Bt this result is transferrable to other systems then broadband linear ∼ should be out of phase in stellar rotation by 0.25 – as suggested by polarimetry is likely to be less sensitive to rotation than to large- Fig. 1. Field fine structure complicates the picture; the relationship scale changes in the field strength. will not be precise because B and Bt are global properties, and With HIPPI we have a superior sensitivity to q and u Stokes at any given phase it is not the same stellar disc presented to the parameters than spectropolarimetry (Cotton et al. 2017b), and we observer. easily detect the time-varying magnetic field in ξ BooA.Inthepast We fit a sinusoid with the equation: broadband linear polarimetry has been used in conjunction with cir- cular polarimetry to more precisely describe the magnetic fields of y(t) = y0 + A sin 2π (t − t0) /T , (3) A- and B-type stars (e.g. Wade et al. 1996). Similar studies may now √of fixed period T = 6.43dseparatelytoeachofthetwodatasets: be made of the magnetic fields of cool stars. Alternatively, magnetic ∝ pˆ (assumed Bt)andB, by allowing the offset y0, the amplitude field maps produced with spectropolarimetry might be used to pre- A and the phase t0 to vary. The fit coefficients and their uncertainties dict the associated broadband linear polarization for the purposes are shown in Table 5. The phase of the HIPPI polarization measure- of subtracting it to reveal other phenomena. For this application ei- ments is 4.50 ± 0.32 d which agrees well with the quarter-shifted ther simultaneous measurements or a stable field would be required. NARVAL phase of 4.40 ± 0.23 d as shown in Fig. 3. To provide More generally, the magnitude of linear polarization to expect in an a simple check of this finding we cross-correlated the maximum active star might be predicted from a determination of B if mod- likelihood fit to the NARVAL data with the square root of the time- els are developed to describe differential saturation in a star with a shifted first cycle of the HIPPI fit (i.e. those shown in Fig. 1), after weak global magnetic field. Follow up work is needed to develop first taking the minimum values as zero and normalizing. This gave such models. In particular the influence of spectral type should be a maximum for a shift of −4.64 d, equivalent to a forward shift of examined in light of Saar & Huovelin (1993)’s prediction of greater ∼0.28 in phase√ units. polarization in later spectral types where there are more spectral ∼ The ratio of pˆ/B in y0 is 0.68, which implies the efficiency lines. √of differential saturation. Naively one might expect that the ratio Searching for polarization from Rayleigh scattering particles in a pˆ/B would be the same for y0 and A; Fig. 3 shows clearly it is hot Jupiter atmosphere in the combined light of the star and planet ∼ 1 not. In fact, from Table 5 A/y0 is 2 in the NARVAL√ data but only is a difficult prospect (Wiktorowicz & Nofi 2015;Bottetal.2018). ∼ 1 6 in the HIPPI data. The relative amplitude in pˆ is depressed In the best case, an orbital period-modulated signal will have an compared to B. amplitude of up to a few 10s of ppm (Seager et al. 2000; Bailey et al. 2018). Such close systems are rare, of those known we estimate only 10–20 are bright enough to be accessible from large telescopes. 4 DISCUSSION Activity has the potential to obfuscate any planetary signal. As an The linear polarization measured in ξ Boo A is rotationally mod- example, consider τ Boo, which has an expected planetary signal of ulated and 0.25 out of phase with the longitudinal magnetic field up to 8 ppm: in their linear polarimetric observations of the system measured by spectropolarimetry, something which would not be ex- Lucas et al. (2009) noted that the data displayed increased scatter, pected from a strong field localized within starspots on the surface and suggested activity could be the cause. τ Boo has a value of (Huovelin & Saar 1991), nor hotspots (Schwarz & Clarke 1984; |B|max of just 4.6 ± 0.4 G (Fares et al. 2009;Mengeletal.2016), Clarke & Schwarz 1984). So, the bulk of the linear polarization but if the relationship found here for ξ Boo A holds this could result signal is due to the weaker global magnetic field. Differences in in a mean linear polarization of 10–20 ppm, albeit with a periodic the fine detail of the two data sets may be easily explained by field variability only some fraction of that. fine structure, but might also be in part due to evolution of the Many other promising close hot Jupiter systems are known to field between the acquisition of the two data sets. We cannot rule be active, including HD 179949 (Fares et al. 2012), WASP 121 out a small contribution from starspots breaking the disc symme- (Delrez et al. 2016), WASP 19 (Huitson et al. 2013), and υ And try. However, modelling by Kostogryz, Yakobchuk & Berdyugina and HD 209458 (Shkolnik et al. 2005). However, the system for (2015) shows that for a star with a G7V spectral type, less than which this result is most relevant is HD 189733, which has been ∼1 ppm is expected from this process. Even for a cooler star with a favoured by groups looking for hot Jupiter polarization (Berdyugina spot covering 5 per cent of the disc, this will not exceed a few ppm. et al. 2011; Wiktorowicz et al. 2015;Bottetal.2016). HST albedo Only in very densely spotted stars will it be higher (Yakobchuk & measurements revealed the planet’s blue colour (Evans et al. 2013) Berdyugina 2018). making it a promising target, with an expected peak polarization ∼ The suppression of linear polarization√ variations relative to what of 20 ppm (Bailey et al. 2018). Yet it is known to be a fairly might be expected from B ∝ p is probably a consequence of active BY Dra variable with a field that evolves over time (Fares geometry. If the largest contributions to the net magnetic field are et al. 2017). Measurements made by Petit et al. (2014)givea|B|max radial, then the strongest contributing surface regions to Bt will be value of 17.3 ± 0.7 G (see also Fares et al. 2017), which could easily at the limb where the intensity is reduced. Leroy (1990) describes translate to a linear polarization of many tens of ppm. Indeed, Bott

MNRAS 483, 1574–1581 (2019) 1580 D. V. Cotton et al. et al. (2016) describe a polarization offset for HD 189733 larger than Bott K., Bailey J., Cotton D. V., Kedziora-Chudczer L., Marshall J. P., expected for interstellar polarization. As that data come from just a Meadows V. S., 2018, AJ, 156, 293 few short runs, stellar activity could easily be the cause. Clearly, it Bott K., Bailey J., Kedziora-Chudczer L., Cotton D. V.,Lucas P.W., Marshall will be necessary to consider strategies for dealing with the star’s J. P., Hough J. H., 2016, MNRAS, 459, L109 activity if a definitive polarimetric detection of the planet is to be Brooks A., Clarke D., McGale P. A., 1994, Vistas Astron., 38, 377 Carroll T. A., Strassmeier K. G., 2014, A&A, 563, A56 made. At the very least, data sets separated in time should not be Downloaded from https://academic.oup.com/mnras/article-abstract/483/2/1574/5218518 by University of Southern Queensland user on 14 November 2019 Clarke D., Schwarz H. E., 1984, A&A, 132, 375 combined without allowing for the potential of long term changes Cotton D. V., Bailey J., Kedziora-Chudczer L., Bott K., Lucas P. W., Hough in the magnetic field producing an offset. J. H., Marshall J. P., 2016a, MNRAS, 455, 1607 Cotton D. V.,Bailey J., Howarth I. D., Bott K., Kedziora-Chudczer L., Lucas 5 CONCLUSIONS P. W., Hough J. H., 2017a, Nature Astron., 1, 690 Cotton D. V., Marshall J. P., Bailey J., Kedziora-Chudczer L., Bott K., We have observed rotationally modulated broadband linear polar- Marsden S. C., Carter B. D., 2017b, MNRAS, 467, 873 ization in ξ Boo A with a characteristic variability of 10–14 ppm. Cotton D. V. et al., 2018, MNRAS, preprint (arXiv:1812.00294) The signal is out of phase by 0.25 with contemporaneous circu- Delrez L. et al., 2016, MNRAS, 458, 4025 lar spectropolarimetric measurements of the longitudinal global Donahue R. A., Saar S. H., Baliunas S. L., 1996, ApJ, 466, 384 magnetic field. 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